2-Local derivations on generalized Witt algebras
Shavkat AyupovDepartment of Mathematics, National University of Uzbekistan, Tashkent, UzbekistanKarimbergen KudaybergenovDepartment of Mathematics, Karakalpak State University, Nukus, UzbekistanBakhtiyor YusupovDepartment of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
ABI
Аннотация
In the present paper, we study 2-local derivations on the so-called infinite dimensional generalized Witt algebras. Firstly, we prove that every 2-local derivation on the generalized Witt algebra Wn(F) over the vector space Fn is a derivation, where F is a field of characteristic zero. Further we consider generalized Witt algebras of the form W=W(G,I) over the field F, where I is an infinite index set and G=⨁i∈IZ=(ai)i∈I:ai=0 except for a finite number of i∈I, and prove that all 2-local derivations on W(G,I) are also derivations. Finally, we show that every 2-local derivation on B(Zn,I), the Borel subalgebra of Wn(F), is a derivation.
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